Correlation Function at $\beta_t$ in the Disordered Phase of 2D Potts Models

TL;DR

This paper uses Monte Carlo simulations to accurately measure the correlation length in the disordered phase of 2D Potts models with high q values, confirming an analytic formula and aligning with large q expansion results.

Contribution

It introduces improved Monte Carlo methods to precisely determine correlation lengths and energy moments in high-q 2D Potts models at the first-order transition.

Findings

Correlation lengths agree with analytic formulas.

Energy moments match large q expansion predictions.

Cluster-update techniques improve measurement accuracy.

Abstract

We use Monte Carlo simulations to measure the spin-spin correlation function in the disordered phase of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ at the first-order transition point $\beta_t$. To extract the correlation length $\xi_d$ from the exponential decay of the correlation function over several decades with the desired accuracy we make extensively use of cluster-update techniques and improved estimators. Our results for $\xi_d$ are compatible with an analytic formula. As a byproduct we also measure the energy moments in the disordered phase and find very good agreement with a recent large $q$ expansion at $\beta_t$.